- #1
reenmachine
Gold Member
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Homework Statement
Use the binomial theorem to find the coefficient of ##x^6y^3## in ##(3x-2y)^9##.
Homework Equations
##1+9+36+84+126+126+84+36+9+1##
(I used two lines for the lenght)
##1(3x)^9(-2y)^0+9(3x)^8(-2y)^1+36(3x)^7(-2y)^2+84(3x)^6(-2y)^3+126(3x)^5(-2y)^4##
##+126(3x)^4(-2y)^5+84(3x)^3(-2y)^6+36(3x)^2(-2y)^7+9(3x)^1(-2y)^8+1(3x)^0(-2y)^9##
(again using two lines because of the lenght)
##19683x^9 - 118098x^8y + 314928x^7y^2 -489888x^6y^3 +489888x^5y^4 -326592x^4y^5##
##+145152x^3y^6 - 41472x^2y^7 +6912xy^8 -512y^9##
So the coefficient of ##x^6y^3## would be ##-489888##
any help will be greatly appreciated! thank you!